Separating data from errors and noise has always been a critical and important problem in signal processing, computer vision and data mining. Robust principal component pursuit is particularly successful in recovering low dimensional structures of high dimensional data from arbitrary sparse outliers. However, successful applications of sparse models in computer vision and machine learning have increasingly hinted at a more general model, namely that the underlying structure of high dimensional data looks more like a union of subspaces (UoS) rather than a single low dimensional subspace. Therefore, it is desired to extend such techniques to high dimensional data modeling where the union of subspaces is further impacted by outliers and errors. This problem is intrinsically difficult, since the underlying subspace structure may be corrupted by unknown errors which, in turn, may lead to unreliable measurement of distance among data samples and cause data to deviate from the original subspaces.